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Volume 27, Issue 2
Existence and Nonexistence of Weak Positive Solution for a Class of p-Laplacian Systems

Kamel Akrout & Rafik Guefaifia

DOI: 10.4208/jpde.v27.n2.6

J. Part. Diff. Eq., 27 (2014), pp. 158-165.

Published online: 2014-06

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  • Abstract
In this work, we are interested to obtain some result of existence and nonexistence of positive weak solution for the following p-Laplacian system $$\begin{equation}\begin{case}-Δ_{pi}u_i=λ_if_i (u_1,…,u_m),\qquad in\;Ω,\;\;i=1,…,m,\\ui=0,\qquad on ∂Ω,\;\;∀i=1,…,m,\end{case}\end{equation}$$ where Δ_{pi}z=div(|∇z|^{pi-2}∇z), pi ≥ 1,λ_i,1 ≤ i ≤ m are a positive parameter, and Ω is a bounded domain in \mathbb{R}^N with smooth boundary ∂Ω. The proof of the main results is based to the method of sub-supersolutions.
  • Keywords

Positive solutions sub-supersolutions elliptic systems

  • AMS Subject Headings

35J25, 35J60

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

akroutkamel@gmail.com (Kamel Akrout)

nabilrad12@yahoo.fr (Rafik Guefaifia)

  • BibTex
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  • TXT
@Article{JPDE-27-158, author = {Akrout , Kamel and Guefaifia , Rafik}, title = {Existence and Nonexistence of Weak Positive Solution for a Class of p-Laplacian Systems}, journal = {Journal of Partial Differential Equations}, year = {2014}, volume = {27}, number = {2}, pages = {158--165}, abstract = {In this work, we are interested to obtain some result of existence and nonexistence of positive weak solution for the following p-Laplacian system $$\begin{equation}\begin{case}-Δ_{pi}u_i=λ_if_i (u_1,…,u_m),\qquad in\;Ω,\;\;i=1,…,m,\\ui=0,\qquad on ∂Ω,\;\;∀i=1,…,m,\end{case}\end{equation}$$ where Δ_{pi}z=div(|∇z|^{pi-2}∇z), pi ≥ 1,λ_i,1 ≤ i ≤ m are a positive parameter, and Ω is a bounded domain in \mathbb{R}^N with smooth boundary ∂Ω. The proof of the main results is based to the method of sub-supersolutions.}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v27.n2.6}, url = {http://global-sci.org/intro/article_detail/jpde/5133.html} }
TY - JOUR T1 - Existence and Nonexistence of Weak Positive Solution for a Class of p-Laplacian Systems AU - Akrout , Kamel AU - Guefaifia , Rafik JO - Journal of Partial Differential Equations VL - 2 SP - 158 EP - 165 PY - 2014 DA - 2014/06 SN - 27 DO - http://doi.org/10.4208/jpde.v27.n2.6 UR - https://global-sci.org/intro/article_detail/jpde/5133.html KW - Positive solutions KW - sub-supersolutions KW - elliptic systems AB - In this work, we are interested to obtain some result of existence and nonexistence of positive weak solution for the following p-Laplacian system $$\begin{equation}\begin{case}-Δ_{pi}u_i=λ_if_i (u_1,…,u_m),\qquad in\;Ω,\;\;i=1,…,m,\\ui=0,\qquad on ∂Ω,\;\;∀i=1,…,m,\end{case}\end{equation}$$ where Δ_{pi}z=div(|∇z|^{pi-2}∇z), pi ≥ 1,λ_i,1 ≤ i ≤ m are a positive parameter, and Ω is a bounded domain in \mathbb{R}^N with smooth boundary ∂Ω. The proof of the main results is based to the method of sub-supersolutions.
Kamel Akrout & Rafik Guefaifia. (2019). Existence and Nonexistence of Weak Positive Solution for a Class of p-Laplacian Systems. Journal of Partial Differential Equations. 27 (2). 158-165. doi:10.4208/jpde.v27.n2.6
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